let G1 be _Graph; :: thesis: for G2 being G1 -isomorphic _Graph

for G3 being SimpleGraph of G1

for G4 being SimpleGraph of G2 holds G4 is G3 -isomorphic

let G2 be G1 -isomorphic _Graph; :: thesis: for G3 being SimpleGraph of G1

for G4 being SimpleGraph of G2 holds G4 is G3 -isomorphic

let G3 be SimpleGraph of G1; :: thesis: for G4 being SimpleGraph of G2 holds G4 is G3 -isomorphic

let G4 be SimpleGraph of G2; :: thesis: G4 is G3 -isomorphic

set G5 = the removeLoops of G1;

set G6 = the removeLoops of G2;

A1: the removeLoops of G2 is the removeLoops of G1 -isomorphic by Th166;

( G3 is removeParallelEdges of the removeLoops of G1 & G4 is removeParallelEdges of the removeLoops of G2 ) by GLIB_009:121;

hence G4 is G3 -isomorphic by A1, Th168; :: thesis: verum

for G3 being SimpleGraph of G1

for G4 being SimpleGraph of G2 holds G4 is G3 -isomorphic

let G2 be G1 -isomorphic _Graph; :: thesis: for G3 being SimpleGraph of G1

for G4 being SimpleGraph of G2 holds G4 is G3 -isomorphic

let G3 be SimpleGraph of G1; :: thesis: for G4 being SimpleGraph of G2 holds G4 is G3 -isomorphic

let G4 be SimpleGraph of G2; :: thesis: G4 is G3 -isomorphic

set G5 = the removeLoops of G1;

set G6 = the removeLoops of G2;

A1: the removeLoops of G2 is the removeLoops of G1 -isomorphic by Th166;

( G3 is removeParallelEdges of the removeLoops of G1 & G4 is removeParallelEdges of the removeLoops of G2 ) by GLIB_009:121;

hence G4 is G3 -isomorphic by A1, Th168; :: thesis: verum